Background

Cost-Benefit Analysis (CBA) estimates and
totals up the equivalent money value of the benefits and costs to the
community of projects to establish whether they are worthwhile. These
projects may be dams and highways or can be training programs and health
care systems.

The idea of this economic accounting originated with Jules Dupuit, a
French engineer whose 1848 article is still worth reading. The British
economist, Alfred Marshall, formulated some of the formal concepts that are at the
foundation of CBA. But the practical development of CBA came as a result
of the impetus provided by the Federal Navigation Act of 1936. This act
required that the U.S. Corps of Engineers carry out projects for the
improvement of the waterway system when the total benefits of a project
to whomsoever they accrue exceed the costs of that project. Thus,
the Corps of Engineers had created systematic methods for measuring such
benefits and costs. The engineers of the Corps did this without much, if
any, assistance from the economics profession. It wasn't until about twenty
years later in the 1950's that economists tried to provide a rigorous,
consistent set of methods for measuring benefits and costs and deciding
whether a project is worthwhile. Some technical issues of CBA have not
been wholly resolved even now but the fundamental presented in the following
are well established.

Principles of Cost Benefit Analysis

One of the problems of CBA is that the computation of many components of
benefits and costs is intuitively obvious but that there are others for
which intuition fails to suggest methods of measurement. Therefore some
basic principles are needed as a guide.

There Must Be a Common Unit of Measurement

In order to reach a conclusion as to the desirability of a project all
aspects of the project, positive and negative, must be expressed in terms
of a common unit; i.e., there must be a "bottom line." The most convenient
common unit is money. This means that all benefits and costs of a project
should be measured in terms of their equivalent money value. A program may
provide benefits which are not directly expressed in terms of dollars but
there is some amount of money the recipients of the benefits would consider
just as good as the project's benefits. For example, a project may provide
for the elderly in an area a free monthly visit to a doctor. The value of
that benefit to an elderly recipient is the minimum amount of money that
that recipient would take instead of the medical care. This could be less
than the market value of the medical care provided. It is assumed that more
esoteric benefits such as from preserving open space or historic sites have
a finite equivalent money value to the public.

Not only do the benefits and costs of a project have to be expressed in
terms of equivalent money value, but they have to be expressed in terms of
dollars of a particular time. This is not just due to the differences in
the value of dollars at different times because of inflation. A dollar
available five years from now is not as good as a dollar available now.
This is because a dollar available now can be invested and earn interest
for five years and would be worth more than a dollar in five years. If the
interest rate is r then a dollar invested for t years will grow to be
(1+r)t. Therefore the amount of money that would have to be
deposited now so that it would grow to be one dollar t years in the
future is (1+r)-t. This called the discounted value or present
value of a dollar available t years in the future.

When the dollar value of benefits at some time in the future is
multiplied by the discounted value of one dollar at that time in the future
the result is discounted present value of that benefit of the project. The
same thing applies to costs. The net benefit of the projects is just the
sum of the present value of the benefits less the present value of the costs.

The choice of the appropriate interest rate to use for the discounting is
a separate issue that will be treated later in this paper.

CBA Valuations Should Represent Consumers or Producers Valuations As
Revealed by Their Actual Behavior

The valuation of benefits and costs should reflect preferences revealed
by choices which have been made. For example, improvements in transportation
frequently involve saving time. The question is how to measure the money
value of that time saved. The value should not be merely what transportation
planners think time should be worth or even what people say their
time is worth. The value of time should be that which the public reveals
their time is worth through choices involving tradeoffs between time and
money. If people have a choice of parking close to their destination for a
fee of 50 cents or parking farther away and spending 5 minutes more walking
and they always choose to spend the money and save the time and effort
then they have revealed that their time is more valuable to them than 10 cents
per minute. If they were indifferent between the two choices they would have
revealed that the value of their time to them was exactly 10 cents per
minute.

The most challenging part of CBA is finding past choices which reveal
the tradeoffs and equivalencies in preferences. For example, the valuation
of the benefit of cleaner air could be established by finding how much less
people paid for housing in more polluted areas which otherwise was identical
in characteristics and location to housing in less polluted areas. Generally
the value of cleaner air to people as revealed by the hard market choices
seems to be less than their rhetorical valuation of clean air.

Benefits Are Usually Measured by Market Choices

When consumers make purchases at market prices they reveal
that the things
they buy are at least as beneficial to them as the money they relinquish.
Consumers will increase their consumption of any commodity up to the point
where the benefit of an additional unit (marginal benefit) is equal to the
marginal cost to them of that unit, the market price. Therefore for any
consumer buying some of a commodity, the marginal benefit is equal to the
market price. The marginal benefit will decline with the amount consumed
just as the market price has to decline to get consumers to consume a greater
quantity of the commodity. The relationship between the market price and
the quantity consumed is called the demand schedule. Thus the demand
schedule provides the information about marginal benefit that is needed to
place a money value on an increase in consumption.

Gross Benefits of an Increase in Consumption is an Area Under the
Demand Curve

The increase in benefits resulting from an increase in
consumption is the sum of the marginal benefit times each incremental
increase in consumption. As the incremental increases considered are taken
as smaller and smaller the sum goes to the area under the marginal benefit
curve. But the marginal benefit curve is the same as the demand curve so
the increase in benefits is the area under the demand curve. As shown in
Figure 1 the area is over the range from the lower limit of consumption
before the increase to consumption after the increase.

Figure 1

When the increase in consumption is small compared to the total
consumption the gross benefit is adequately approximated, as is shown
in a welfare analysis, by the market value of the increased consumption; i.e., market
price times the increase in consumption.

Some Measurements of Benefits Require the Valuation of Human Life

It is sometimes necessary in CBA to evaluate the benefit of saving human
lives. There is considerable antipathy in the general public to the idea
of placing a dollar value on human life. Economists recognize that it is
impossible to fund every project which promises to save a human life and
that some rational basis is needed to select which projects are approved
and which are turned down. The controversy is defused when it is recognized
that the benefit of such projects is in reducing the risk of death. There
are many cases in which people voluntarily accept increased risks in return
for higher pay, such as in the oil fields or mining, or for time savings in
higher speed in automobile travel. These choices can be used to estimate
the personal cost people place on increased risk and thus the value to them
of reduced risk. This computation is equivalent to placing an economic
value on the expected number of lives saved.

The Analysis of a Project Should Involve a With Versus Without
Comparison

The impact of a project is the difference between what
the situation in the study area would be with and without the project. This
that when a project is being evaluated the analysis must estimate not only
what the situation would be with the project but also what it would be
without the project. For example, in determining the impact of a fixed
guideway rapid transit system such as the Bay Area Rapid Transit (BART) in
the San Francisco Bay Area the number of rides that would have been taken
on an expansion of the bus system should be deducted from the rides provided
by BART and likewise the additional costs of such an expanded bus system
would be deducted from the costs of BART. In other words, the alternative
to the project must be explicitly specified and considered in the evaluation
of the project. Note that the with-and-without comparison is not the same
as a before-and-after comparison.

Another example shows the importance of considering the impacts of a
project and a with-and-without comparison. Suppose an irrigation project
proposes to increase cotton production in Arizona. If the United States
Department of Agriculture limits the cotton production in the U.S. by a
system of quotas then expanded cotton production in Arizona might be offset
by a reduction in the cotton production quota for Mississippi. Thus the
impact of the project on cotton production in the U.S. might be zero rather
than being the amount of cotton produced by the project.

Cost Benefit Analysis Involves a Particular Study Area

The impacts of a project are defined for a particular study area, be it
a city, region, state, nation or the world. In the above example concerning
cotton the impact of the project might be zero for the nation but still be
a positive amount for Arizona.

The nature of the study area is usually specified by the organization
sponsoring the analysis. Many effects of a project may "net out" over one
study area but not over a smaller one. The specification of the study area
may be arbitrary but it may significantly affect the conclusions of the
analysis.

Double Counting of Benefits or Costs Must be Avoided

Sometimes an impact of a project can be measured in two or more ways.
For example, when an improved highway reduces travel time and the risk of
injury the value of property in areas served by the highway will be enhanced.
The increase in property values due to the project is a very good way, at least
in principle, to measure the benefits of a project. But if the increased
property values are included then it is unnecessary to include the value
of the time and lives saved by the improvement in the highway. The property
value went up because of the benefits of the time saving and the reduced
risks. To include both the increase in property values and the time saving
and risk reduction would involve double counting.

Decision Criteria for Projects

If the discounted present value of the benefits exceeds the discounted
present value of the costs then the project is worthwhile. This is
equivalent to the condition that the net benefit must be positive.
Another equivalent condition is that the ratio of the present value of
the benefits to the present value of the costs must be greater than one.

If there are more than one mutually exclusive project that have positive
net present value then there has to be further analysis. From the set
of mutually exclusive projects the one that should be selected is the
one with the highest net present value.

If the funds required for carrying out all of the projects with positive net
present value are less than the funds available this means the discount rate
used in computing the present values is too low and does not reflect the true
cost of capital. The present values must be recomputed using a higher
discount rate. It may take some trial and error to find a discount rate such
that the funds required for the projects with a positive net present value is
no more than the funds available. Sometimes as an alternative to this
procedure people try to select the best projects on the basis of some measure
of goodness such as the internal rate of return or the benefit/cost ratio.
This is not valid for several reasons.

The magnitude of the ratio of benefits to costs is to a degree arbitrary
because some costs such as operating costs may be deducted from benefits and
thus not be included in the cost figure. This is called netting out of operating costs.
This netting out may be done for some projects
and not for others. This manipulation of the benefits and costs will not
affect the net benefits but it may change the benefit/cost ratio. However it will not raise
the benefit cost ratio which is
less than one to above one. For more on this topic see Benefit/
cost Ratio Magnitude.

To illustrate how CBA might be applied to a project, let us consider a
highway improvement such as the extension of Highway 101 into San Jose. The
local four-lane highway which carried the freeway and commuter traffic into
San Jose did not have a median divider and its inordinate number of fatal head-on
collisions led to the name "Blood Alley." The improvement of the highway
would lead to more capacity which produces time saving and lowers the risk.
But inevitably there will be more traffic than was carried by the old
highway.

The following is a highly abbreviated analysis using hypothetical data.

TRIP DATA

No Extension,"Blood Alley" Only

101 Extensionand "Blood Alley"

Rush Hours

Passenger Trips (per hour)

3,000

4,000

Trip Time (minutes)

50

30

Value of Time ($/minute)

$0.10

$0.10

Nonrush Hours

Passenger Trips (per hour)

500

555.55

Trip Time (minutes)

35

25

Value of Time ($/minute)

$0.08

$0.08

Traffic Fatalities (per year)

12

6

The data indicates that for rush-hour trips the time cost of a trip is $5 without the project
and $3 with it. It is assumed that the operating cost for a vehicle is
unaffected by the project and is $4.

The project lowers the cost of a trip and the public responds by increasing
the number of trips taken. There is an increase in consumer surplus both
for the trips which would have been taken without the project and for the
trips which are stimulated by the project.

For trips which would have been taken anyway the benefit of the project
equals the value of the time saved times the number of trips. For the
rush-hour trip the project saves $2 and for the nonrush-hour trip it saves
$0.80. For the trips generated by the project the benefit is equal to
one half of the value of the time saved times the increase in the number
of trips.

The benefits per hour are:

TYPE

Trips Which WouldBe Taken Anyway

Trips GeneratedBy the
Project

Total

Rush Hour

6,000.00

1,000.00

7,000.00

Nonrush Hour

400.00

22.22

422.22

To convert the benefits to an annual basis one multiplies the hourly
benefits of each type of trip times the number of hours per year for that
type of trip. There are 260 week days per year and at six rush hours per
weekday there are 1560 rush hours per year. This leaves 7200 nonrush hours
per year. With these figures the annual benefits are:

TYPE

Trips WhichWould BeTaken Anyway

Trips GeneratedBy the
Project

Total

Rush Hour

$9,360,000

$1,560,000

$10,020,000

Nonrush Hour

$2,880,000

$160,000

$3,040,000

Total

$12,240,000

$1,720,000

$13,960,000

The value of the reduced fatalities may be computed in terms of the
equivalent economic value people place upon their lives when making choices
concerning risk and money. If the labor market has wages for occupations
of different risks such that people accept an increase in the risk of
death of 1/1,000 per year in return for an increase in income of $400 per
year then a project that reduces the risk of death in a year by 1/1000
gives a benefit to each person affected by it of $400 per year. The
implicit valuation of a life in this case is $400,000. Thus benefit of the
reduced risk project is the expected number of lives saved times the
implicit value of a life. For the highway project this is 6x$400,000=
$2,400,000 annually.

The annual benefits of the project are thus:

TYPE OF BENEFIT

VALUE OF BENEFITSPER YEAR

Time Saving

$13,960,000

Reduced Risk

$2,400,000

Let us assume that this level of benefits continues at a constant rate
over a thirty-year lifetime of the project.

The cost of the highway consists of the costs for its right-of-way,
its construction and its maintenance. The cost of the right-of-way is
the cost of the land and any structures upon it which must be purchased
before the construction of the highway can begin. For purposes of this
example the cost of right-of-way is taken to be $100 million and it must
be paid before any construction can begin. At least part of the right-of-
way cost for a highway can be recovered at the end of the lifetime of the
highway if it is not rebuilt. For the example it is assumed that all of
the right-of-way cost is recoverable at the end of the thirty-year lifetime
of the project. The construction cost is $200 million spread evenly over
a four-year period. Maintenance cost is $1 million per year once the highway
is completed.

The schedule of benefits and costs for the project are as follows:

TIME(year)

BENEFITS($millions)

RIGHT-OF-WAY
($millions)

CONSTRUCTIONCOSTS($millions)

MAINTENANCE($millions)

0

0

100

0

0

1-4

0

0

50

0

5-29

16.36

0

0

1

30

16.36

-100

0

1

The benefits and costs are in constant value dollars; i.e., there was
no price increase included in the analysis. Therefore the discount rate
used must be the real interest rate. If the interest rate on long term
bonds is 8 percent and the rate of inflation is 6 percent then the real
rate of interest is 2 percent. Present value of the streams of benefits
and costs discounted at a 2 percent back to time zero are as follows:

PRESENT
VALUE($ millions)

Benefits

304.11

Costs

Right-of-Way

44.79

Construction

190.39

Maintenance

18.59

Total Costs

253.77

Net Benefits

50.35

*independent rounding

The positive net present value of $50.35 million and benefit/cost ratio
of 1.2 indicate that the project is worthwhile if the cost of capital is
2 percent. When a discount rate of 3 percent is the benefit/cost ratio
is slightly under 1.0. This means that the internal rate of return is just
under 3 percent. When the cost of capital is 3 percent the project is not
worthwhile.

It should be noted that the market value of the right-of-way understates
the opportunity cost of having the land devoted to the highway. The land
has a value of $100 million because of its income after property taxes.
The economy is paying more for its alternate use but some of the payment
is diverted for taxes. The discounted presented value of the payments for
the alternate use might be more like $150 million instead of $100 million.
Another way of making this point is that one of the costs of the highway is
that the local governments lose the property tax on the land used.

Summary

By reducing the positive and negative impacts of a project to their
equivalent money value Cost-Benefit Analysis determines whether on balance
the project is worthwhile. The equivalent money value are based upon
information derived from consumer and producer market choices; i.e., the
demand and supply schedules for the goods and services affected by the
project. Care must be taken to properly allow for such things as inflation.
When all this has been considered a worthwhile project is one for which the
discounted value of the benefits exceeds the discounted value of the
costs; i.e., the net benefits are positive. This is equivalent to the
benefit/cost ratio being greater than one and the internal rate of return
being greater than the cost of capital.

CBA has its origins in the water development projects of the
U.S. Army Corps of Engineers. The Corps of Engineers had its
origins in the French engineers hired by George Washington in
the American Revolution. For years the only school of
engineering in the United States was the Military Academy at
West Point, New York.

In 1879, Congress created the Mississippi River Commission
to "prevent destructive floods." The Commission included
civilians but the president had to be an Army engineer and
the Corps of Engineers always had veto power over any decision
by the Commission.

In 1936 Congress passed the Flood Control Act which contained
the wording, "the Federal Government should improve or
participate in the improvement of navigable waters or their
tributaries, including watersheds thereof, for flood-control
purposes if the benefits to whomsoever they may accrue are in
excess of the estimated costs." The phrase if the benefits
to whomsoever they may accrue are in excess of the estimated
costs established cost-benefit analysis. Initially the
Corps of Engineers developed ad hoc methods for estimating
benefits and costs. It wasn't until the 1950s that academic
economists discovered that the Corps had developed a system
for the economic analysis of public investments. Economists
have influenced and improved the Corps' methods since then and
cost-benefit analysis has been adapted to most areas of public
decision-making.